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B - The binary system

Published online by Cambridge University Press:  06 July 2010

Peter R. Hoskins
Affiliation:
University of Edinburgh
Kevin Martin
Affiliation:
University of Leicester
Abigail Thrush
Affiliation:
St Bartholomew's Hospital, London
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Summary

A number in the decimal system consists of several digits, each representing a quantity of units, 10s or 100s, etc. For example, the decimal number 6473 represents 6 thousands plus 4 hundreds plus 7 tens plus 3 units. The value of 1 count in each column is a power of 10, i.e. 1 × 100 = 102, 1 × 1000 = 103. The maximum count of a 4-digit number is 9999. When counting from zero, the digit in the right-hand column (units) is increased until it reaches 9, and on the next count it returns to 0, while the digit in the 10s column is increased by 1. Each column carries over into the next to the left after a count of 9. The binary system operates in an identical fashion but the value of one count in each column is a power of 2, e.g. 23, 22, 21, 20. In decimal terms, the values of the digits are 8, 4, 2 and 1, and the maximum count in each column is 1. So the maximum value for a 4-digit number is 1111, which is 15 in decimal. Counting from 0, the digit on the right (20 column) changes from 0 to 1. On the next count, it goes back to 0 and the digit to the left (21 column) goes from 0 to 1.

Type
Chapter
Information
Diagnostic Ultrasound
Physics and Equipment
, pp. 216
Publisher: Cambridge University Press
Print publication year: 2010

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